Well technically a fb is an email account so does that mean u can't have a fb or other email accounts and if u want a fb/email make 1 and don't tell it parents as long as they don't ask it cool plus u can put urself under a diff name and tell ur friends that name easy! :D
It's disgusting to see that there are those here who would encourage your dishonesty. Find out what your parents fears are about. After all their are a lot of weirdos out there that misuse a great tool to harm you. Learn how the privacy settings work under account settings. It is possible to use facebook only with friends you know. You can choose not to be public. Remember though, If you post on your friends wall and they have public accounts non-friends and strangers will be able to see you on the friends wall. But you will still have the option to refuse any query. Get your parents to learn this with you, maybe their fears will subside. But if they say ok you must stick to what ever you agree to with them. This is best even if they still say no.